Acta Crystallographica Section A最新文献

An extension of the X-ray extended-range technique is described for measuring X-ray mass attenuation coefficients by introducing absolute measurement of a number of foils - the multiple independent foil technique. Illustrating the technique with the results of measurements for gold in the 38-50 keV energy range, it is shown that its use enables selection of the most uniform and well defined of available foils, leading to more accurate measurements; it allows one to test the consistency of independently measured absolute values of the mass attenuation coefficient with those obtained by the thickness transfer method; and it tests the linearity of the response of the counter and counting chain throughout the range of X-ray intensities encountered in a given experiment. In light of the results for gold, the strategy to be ideally employed in measuring absolute X-ray mass attenuation coefficients, X-ray absorption fine structure and related quantities is discussed.

p-Periodic nets can be derived from a voltage graph G with voltages in Z(p), the free abelian group of rank p, if the cyclomatic number γ of G is larger than p. Equivalently, one may describe a net by providing a set of (γ - p) cycle vectors of G forming a basis of the subspace of the cycle space of G with zero net voltage. Let M be the matrix of this basis expressed in the edge basis of the 1-chain space of G. A net is called totally unimodular whenever every sub-determinant of M belongs to the set {-1, 0, 1}. Only a finite set of totally unimodular nets can be derived from some finite graph. It is shown that totally unimodular nets are stable under the operation of edge-lattice deletion in a sense that makes them comparable to minimal nets. An algorithm for the complete determination of totally unimodular nets derived from some finite graph is presented. As an application, the full list of totally unimodular nets derived from graphs of cyclomatic numbers 3 and 4, without bridges, is given. It is shown that many totally unimodular nets frequently occur in crystal structures.

Diffractionists usually place the birth of crystallography in 1912 with the first X-ray diffraction experiment of Friedrich, Knipping and Laue. This discovery propelled the mathematical branch of mineralogy to global importance and enabled crystal structure determination. Knowledge of the geometrical structure of matter at atomic resolution had revolutionary consequences for all branches of the natural sciences: physics, chemistry, biology, earth sciences and material science. It is scarcely possible for a single person in a single article to trace and appropriately value all of these developments. This article presents the limited, subjective view of its author and a limited selection of references. The bulk of the article covers the history of X-ray structure determination from the NaCl structure to aperiodic structures and macromolecular structures. The theoretical foundations were available by 1920. The subsequent success of crystallography was then due to the development of diffraction equipment, the theory of the solution of the phase problem, symmetry theory and computers. The many structures becoming known called for the development of crystal chemistry and of data banks. Diffuse scattering from disordered structures without and with partial long-range order allows determination of short-range order. Neutron and electron scattering and diffraction are also mentioned.

It has been argued in our recent papers that the heat of formation of intermetallic compounds is mostly concentrated in the nearest neighbor unlike atom-pair bonds, and that the positive term in Miedema's equation is associated with charge transfer on the bond to maintain electroneutrality. In this paper, taking examples of some well populated crystal-structure types such as MgCu(2), AsNa(3), AuCu(3), MoSi(2) and SiCr(3) types, the effect of such charge transfer on the crystal structures adopted by intermetallic compounds is examined. It is shown that the correlation between the observed size changes of atoms on alloying and their electronegativity differences is supportive of the idea of charge transfer between atoms. It is argued that the electronegativity and valence differences need to be of the required magnitude and direction to alter, through charge transfer, the elemental radius ratios R(A)/R(B) to the internal radius ratios r(A)/r(B) allowed by the structure types. Since the size change of atoms on alloying is highly correlated to how different R(A)/R(B) is from the ideal radius ratio for a structure type, the lattice parameters of intermetallic compounds can be predicted with excellent accuracy knowing R(A)/R(B). A practical application of the approach developed in our recent papers to superalloy design is presented.

The direct methods origin-free modulus sum function [Rius (1993). Acta Cryst. A49, 406-409] includes in its definition the structure factor G(Φ) of the squared crystal structure expressed in terms of Φ, the set of φ phases of the normalized structure factors E's of the crystal structure of unit-cell volume V. Here the simpler sum function variant S'(P) = ∑(H)E(-H)∫(V)δ(P,Δ)(Φ)exp(i2πHr)dV extended over all H reflections is introduced which involves no G's and in which the δ(P,Δ) function corresponds to δ(P) = FT(-1){(E(2)(H) - )exp[iφ(H)(Φ)]} (where FT = Fourier transform) with all values smaller than Δ = 2.5σ(P) equated to zero (σ(2)(P) is the variance of δ(P) calculable from the experimental intensities). The new phase estimates are obtained by Fourier transforming δ(P,Δ). This iterative phasing method (δ recycling) only requires calculation of Fourier transforms at two stages. Since δ(M) ≃ δ(P)/2, similar arguments are valid for δ(M) = FT(-1)[(E(H) - )exp(iφ(H))] from which the corresponding S'(M) phasing function follows.

The history of crystallography has been assessed in the context of the emergence and spread of the molecular theory. The present paper focuses on the 19th century, which saw the emancipation of crystallography as a science sui generis. Around 1800, Laplace's molecularism called the tune in the various sciences (physics, chemistry, biology, crystallography). In crystallography, two schools opposed each other: that of Weiss, in Berlin, and that of Haüy, in Paris. Symmetry proved essential. It will be shown how the lattice theory arose in an essentially molecular framework and how group theory imposed itself. The salt hydrates suggested the idea of (two or more) superimposed molecular lattices. Gradually it became clear that an ultimate lattice theory ought to be atomic. The experiments of Laue, Friedrich and Knipping confirmed that atomic basis.

The theoretical databank of aspherical pseudoatoms (UBDB) was recently extended with over 100 new atom types present in RNA, DNA and in some other molecules of great importance in biology and pharmacy. The atom-type definitions were modified and new atom keys added to provide a more precise description of the atomic charge-density distribution. X-H bond lengths were updated according to recent neutron diffraction studies and implemented in the LSDB program as well as used for modelling the appropriate atom types. The UBDB2011 databank was extensively tested. Electrostatic interaction energies calculated on the basis of the databank of aspherical atom models were compared with the corresponding results obtained directly from wavefunctions at the same level of theory (SPDFG/B3LYP/6-31G** and SPDFG/B3LYP/aug-cc-pVDZ). Various small complexes were analysed to cover most of the different interaction types, i.e. adenine-thymine and guanine-cytosine with hydrogen bonding, guanine-adenine with stacking contacts, and a group of neutral and charged species of nucleic acid bases interacting with amino acid side chains. The energy trends are well preserved (R(2) > 0.9); however the energy values differ between the two methods by about 4 kcal mol(-1) (1 kcal mol(-1) = 4.184 kJ mol(-1)) on average. What is noticeable is that the replacement of one basis set by another in a purely quantum chemical approach leads to the same electrostatic energy difference, i.e. of about 4 kcal mol(-1) in magnitude. The present work opens up the possibility of applying the UBDB2011 for macromolecules that contain DNA/RNA fragments. This study shows that on the basis of the UBDB2011 databank electrostatic interaction energies can be estimated and structure refinements carried out. However, some method limitations are apparent.

The discovery of X-ray diffraction is reviewed from the perspective of the contemporary knowledge in 1912 about the nature of X-rays. Laue's inspiration that led to the experiments by Friedrich and Knipping in Sommerfeld's institute was based on erroneous expectations. The ensuing discoveries of the Braggs clarified the phenomenon (although they, too, emerged from dubious assumptions about the nature of X-rays). The early misapprehensions had no impact on the Nobel Prizes to Laue in 1914 and the Braggs in 1915; but when the prizes were finally awarded after the war, the circumstances of `Laue's discovery' gave rise to repercussions. Many years later, they resulted in a dispute about the `myths of origins' of the community of crystallographers.